If you are using a non monitored wrist strap then you need to test the wrist strap, which you are doing, and test the wrist strap connection. They do not have to be on the same schedule for testing. The reason for testing the wrist strap connection is to ensure that the connection to ground is there. If the wrist strap connection is broken or becomes disconnected due to workstation movement then the resistance to ground would be over the 3.5 megaohm limit. The 3.5 megaohm limit is the total resistance to ground which includes the wrist strap system and the connection to ground. It can be tested separately.
To answer your question directly, yes it would be a non-conformance if it is not tested.